1. Field of the Invention
This invention relates generally to the field of signals analysis, and in one exemplary aspect to an apparatus and method for non-invasively detecting and evaluating signals and waveforms such as those present in the impedance cardiograms, electrocardiograms, and other physiologic parameters of a living subject.
2. Description of Related Technology
The study of the performance and properties of the physiology (including notably the cardiovascular system) of a living subject has proven useful for diagnosing and assessing any number of conditions or diseases within the subject. The performance of the cardiovascular system, including the heart, has characteristically been measured in terms of several different parameters, including the stroke volume and cardiac output of the heart.
Noninvasive estimates of cardiac output (CO) can be obtained using the well known technique of impedance cardiography (ICG). Strictly speaking, impedance cardiography, also known as thoracic bioimpedance or impedance plethysmography, is used to measure the stroke volume (SV) of the heart. As shown in Eqn. (1), when the stroke volume is multiplied by heart rate, cardiac output is obtained.CO=SV×heart rate.   (1)During impedance cardiography, a constant alternating current, with a frequency such as 70 kHz, I(t), is applied across the thorax. The resulting voltage, V(t), is used to calculate impedance. Because the impedance is assumed to be purely resistive, the total impedance, ZT(t), is calculated by Ohm's Law. The total impedance consists generally of a constant base impedance, Zo, and time-varying impedance, Zc(t), as shown in Eqn. (2):
                                          Z            T                    ⁡                      (            t            )                          =                                            V              ⁡                              (                t                )                                                    I              ⁡                              (                t                )                                              =                                    Z              o                        +                                                            Z                  c                                ⁡                                  (                  t                  )                                            .                                                          (        2        )            The time-varying impedance is believed to reflect the change in blood resistivity as it transverses through the aorta.
Stroke volume is typically calculated from one of three well known equations, based on this impedance change:
                                                        Kubicek:                        ⁢                                                  ⁢            SV                    =                                    ρ              ⁡                              (                                                      L                    2                                                        Z                    0                    2                                                  )                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (        3        )                                                                    Sramek:                        ⁢                                                  ⁢            SV                    =                                                    L                3                                            4.25                ⁢                                                                  ⁢                                  Z                  o                                                      ⁢            LVET            ⁢                                          ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                                    ,                            (        4        )                                                      Sramek-Berstein:                    ⁢                                          ⁢          SV                =                  δ          ⁢                                                    (                                  0.17                  ⁢                  H                                )                            3                                      4.25              ⁢                              Z                o                                              ⁢          LVET          ⁢                                                    ⅆ                                  Z                  ⁡                                      (                    t                    )                                                                              ⅆ                                  t                  max                                                      .                                              (        5        )            Where:                L=distance between the inner electrodes in cm,        LVET=ventricular ejection time in seconds,        Zo=base impedance in ohms,        
                    ⅆ                  Z          ⁡                      (            t            )                                      ⅆ                  t          max                      =          magnitude      ⁢                          ⁢      of      ⁢                          ⁢      the      ⁢                          ⁢      largest                  negative      ⁢                          ⁢      derivative      ⁢                          ⁢      of      ⁢                          ⁢      the      ⁢                          ⁢      impedance      ⁢                          ⁢      change        ,                  Zc(t), occurring during systole in ohms/s,        ρ=resistivity of blood in ohms-cm,        H=subject height in cm, and        δ=special weight correction factor.Two key parameters present in Eqns. 3, 4, and 5 above are (i)        
      ⅆ          Z      ⁡              (        t        )                  ⅆ          t      max      and (ii) LVET.These parameters are found from features referred to as fiducial points, that are present in the inverted first derivative of the impedance waveform,
            ⅆ              Z        ⁡                  (          t          )                            ⅆ      t        .As described by Lababidi, Z., et al, “The first derivative thoracic impedance cardiogram,” Circulation, 41:651-658, 1970, the value of
      ⅆ          Z      ⁡              (        t        )                  ⅆ          t      max      is generally determined from the time at which the inverted derivative value has the highest amplitude, also commonly referred to as the “C point”. The value of
      ⅆ          Z      ⁡              (        k        )                  ⅆ          t      max      is calculated as this amplitude value. LVET corresponds generally to the time during which the aortic valve is open. That point in time associated with aortic valve opening, also commonly known as the “B point”, is generally determined as the time associated with the onset of the rapid upstroke (a slight inflection) in
      ⅆ          Z      ⁡              (        t        )                  ⅆ    t  before the occurrence of the C point. The time associated with aortic valve closing, also known as the “X point”, is generally determined as the time associated with the inverted derivative global minimum, which occurs after the C point.
In addition to the foregoing “B”, “C”, and “X” points, the so-called “O point” may be of utility in the analysis of the cardiac muscle. The O point represents the time of opening of the mitral valve of the heart. The O point is generally determined as the time associated with the first peak after the X point. The time difference between aortic valve closing and mitral valve opening is known as the isovolumetric relaxation time, IVRT. However, to date, the O point has not found substantial utility in the stroke volume calculation.
Impedance cardiography further requires recording of the subject's electrocardiogram (ECG) in conjunction with the thoracic impedance waveform previously described. Processing of the impedance waveform for hemodynamic analysis generally requires the use of ECG fiducial points as landmarks. Processing of the impedance waveform is generally performed on a beat-by-beat basis, with the ECG being used for beat detection. In addition, detection of some fiducial points of the impedance signal may require the use of ECG fiducial points as landmarks. Specifically, individual beats are identified by detecting the presence of QRS complexes within the ECG. The peak of the R wave (commonly referred to as the “R point”) in the QRS complex is also detected, as well as the onset of depolarization of the QRS complex (“Q point”).
Under the prior art approaches, the aforementioned beats are scrutinized for artifact (e.g., due to motion of the subject, or other such causes), through comparatively simple rules such as the evaluation of calculated parameter values outside a typical numeric range. For example, consider the well-known “Weissler window”, which defines the X point search interval based upon the heart rate and gender of a given individual; see, Weissler, A. M., Peeler, R. G., Roehll, W. H., “Relationships between left ventricular ejection time, stroke volume, and heart rate in normal individuals and patients with cardiovascular disease”, Am Heart J, 62:367-78, 1961. The Weissler regression equation was based upon 121 normal males, and 90 normal females. Although the relationship between heart rate and LVET is linear for normal individuals, in another work Weissler et. al. found that this relationship does not hold for abnormal patients. In 12 non-valvular CHF patients with COs ranging from 2.1-5.8 L/min, 9 patients had a significant decrease (p<0.05) in ejection time relative to heart rate; see Weissler, A. M., Harris, W S., and Schoenfeld, C. D., “Systolic Time Intervals in Heart Failure in Man. Circulation”, 37:149-59, 1968. Hence, when applying such criteria, the true X points in CHF or other cardiovascular patients may be erroneously rejected because these X points lie outside of the Weissler window.
Other such “parametric” rejection rules may include for example (i) LVET outside of a desired range, (ii) detection of a pacing spike with the left/right values of ΔZ(t) (also referred to as Delta Z), (iii) d2Z/dt2MAX=0, and (iv) dZ/dtMAX=0 (or less than a percentage of the median value of the most recent beats).
Parameter values from the remaining beats (i.e., those not rejected by the aforementioned parametric criteria) are then typically averaged as a mean, based on a beat average number chosen by the user.
Aside from erroneous rejection of beats as described above in the context of the Weissler window, other problems with prior art beat analysis and rejection approaches exist. Specifically, significant instabilities in various of the monitored or derived parameters such as ECG, and left/right ΔZ(t) can result. Such instabilities can reduce both the accuracy and clinical robustness of the measurement process. Erroneous pacing spike detection may also occur during a time interval that does not overlap with a valid B, C, or X point. Additionally, when the electrodes are disconnected, the “flat-line” ECG and Delta Z signals may provide a non-zero cardiac output (CO) estimate.
Still another distinct deficiency with the prior art analysis and rejection schemes relates to their lack of discrimination between different types of subjects. This lack of discrimination has two primary outgrowths: (i) causing the system to simply not function due to being unable to measure one or more necessary parameters; and (ii) imbuing the user or operator with somewhat of a false sense of security that all types of subjects (regardless of their peculiar waveforms, arrhythmias or defects) could be successfully monitored, including generating highly suspect or even erroneous data without otherwise alerting the user as to the potential for degraded accuracy. Without any sort of contraindication (or even metric advising on the confidence level of the data or results), the user/operator has no way of knowing, other than perhaps via innate experience or knowledge, whether any given data is valid or accurate.
Fuzzy Logic and Fuzzy Models
As is well known in the art, so-called “fuzzy logic” is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth; i.e., truth values falling between “completely true” and “completely false”. Fuzzy logic was invented by Dr. Lotfi Zadeh of U.C. Berkeley in 1965. The fuzzy model, which utilizes fuzzy logic, is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data systems. It can be implemented in hardware, software, or a combination of both. The fuzzy model provides a comparatively simple technique for arriving at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information, and in some aspects mimics the human decision making process.
As is well understood in the prior art, a fuzzy model incorporates alternative, rule-based mathematics (e.g., If X AND Y THEN Z), as opposed to attempting to model a system or its response using closed-form mathematical equations. When the number of model inputs and model outputs are limited to two each, the fuzzy model is in general empirically-based, relying on an empirical data (such as prior observations of parameters or even an operator's experience).
Specifically, a subset U of a set S can be defined as a set of ordered pairs, each with a first element that is an element of the set S, and a second element that is an element of the set {0, 1}, with exactly one ordered pair present for each element of S. This relationship defines a mapping between elements of S and elements of the set {0, 1}. Here, the value “0” is used to represent non-membership, and the value “1” is used to represent membership. The truth or falsity of the exemplary statement:A is in Uis determined by finding the ordered pair whose first element is A. The foregoing statement is true if the second element of the ordered pair is “1”, and the statement is false if it is “0”. Similarly, a fuzzy subset F of set S can be defined as a set of ordered pairs, each having a first element that is an element of the set S, and a second element that is a value falling in the interval [0, 1], with exactly one ordered pair present for each element of S. This defines a mapping between elements of the set S and values in the interval [0, 1]. The value zero is used to represent complete non-membership, the value one is used to represent complete membership, and values in between are used to represent intermediate degrees of membership. These fuzzy subsets serve as the fuzzy inputs and outputs of a fuzzy model, whose input-output relationship is defined by a rule base table.
Inherent benefits of the fuzzy model relate to its speed and simplicity of processing (e.g., MIPS, FLOPS, or similar benchmark), and its ability to process data that is not easily represented in closed-form equations, such as may occur in physiologic data. The benefits are particularly useful the analysis of time-variant “noisy” signals where detection, identification, and/or evaluation of one or more features or events of the waveform are required, such as electrocardiography, impedance cardiography, or electroencephalography.
Based on the foregoing, what is needed are improved methods and apparatus for assessing physiologic (e.g., hemodynamic) parameters, including cardiac output, within a living subject. Such method and apparatus would ideally be completely non-invasive, accurate, easily adapted to the varying physiology of different subjects, and would produce reliable and stable results under a variety of different operating conditions. These methods and apparatus would be particularly adapted to processing (and rejecting, where warranted) “noisy” waveforms having events such as cardiac beats, and would allow for monitoring of a broader range of patient types and conditions (including various arrhythmias).